# Re: Wilcoxon Mann-Whitney Rank Sum Test in R

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## Re: Wilcoxon Mann-Whitney Rank Sum Test in R

 An earlier post had posed the question: "Does anybody know what is relation between 'T' value calculated by 'wilcox_test' function (coin package) and more common 'W' value?" I found the question interesting and ran the commands in R and SPSS. The W reported by R did not seem to correspond to either   Mann-Whitney U, Wilcoxon W or the Z which I have more commonly used. Correction for ties may have affected my results. Can anyone else explain what the reported W is and the relation to the reported T? regards bob ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: Wilcoxon Mann-Whitney Rank Sum Test in R

 Bob Green <[hidden email]> writes: > An earlier post had posed the question: "Does anybody know what is relation > between 'T' value calculated by 'wilcox_test' function (coin package) and > more common 'W' value?" > > I found the question interesting and ran the commands in R and SPSS. The W > reported by R did not seem to correspond to either   Mann-Whitney U, > Wilcoxon W or the Z which I have more commonly used. Correction for ties > may have affected my results. > > Can anyone else explain what the reported W is and the relation to the > reported T? Well, it's open source... You could just go check. W is the sum of the ranks in the first group, minus the minimum value it can attain, namely sum(1:n1) == n1*(n1+1)/2. In the tied cases, the actual minimum could be larger. The T would seem to be asymptotically normal > wilcox_test(pd ~ age, data = water_transfer,distribution="asymp")         Asymptotic Wilcoxon Mann-Whitney Rank Sum Test data:  pd by groups 12-26 Weeks, At term T = -1.2247, p-value = 0.2207 alternative hypothesis: true mu is not equal to 0 > pnorm(-1.2247)*2 [1] 0.2206883 so a good guess at its definition is that it is obtained from W or one of the others by subtracting the mean and dividing with the SD. --    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K  (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918 ~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: Wilcoxon Mann-Whitney Rank Sum Test in R

 Peter Dalgaard wrote: > Bob Green <[hidden email]> writes: > > >>An earlier post had posed the question: "Does anybody know what is relation >>between 'T' value calculated by 'wilcox_test' function (coin package) and >>more common 'W' value?" >> >>I found the question interesting and ran the commands in R and SPSS. The W >>reported by R did not seem to correspond to either   Mann-Whitney U, >>Wilcoxon W or the Z which I have more commonly used. Correction for ties >>may have affected my results. >> >>Can anyone else explain what the reported W is and the relation to the >>reported T? > > > Well, it's open source... You could just go check. > > W is the sum of the ranks in the first group, minus the minimum value > it can attain, namely sum(1:n1) == n1*(n1+1)/2. In the tied cases, the > actual minimum could be larger. > > The T would seem to be asymptotically normal > > >>wilcox_test(pd ~ age, data = water_transfer,distribution="asymp") > > >         Asymptotic Wilcoxon Mann-Whitney Rank Sum Test > > data:  pd by groups 12-26 Weeks, At term > T = -1.2247, p-value = 0.2207 > alternative hypothesis: true mu is not equal to 0 > > >>pnorm(-1.2247)*2 > > [1] 0.2206883 > > so a good guess at its definition is that it is obtained from W or one > of the others by subtracting the mean and dividing with the SD. > With the SD adjusted for ties, of course. (See, e.g., Conover's book.) Peter Ehlers University of Calgary ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: Wilcoxon Mann-Whitney Rank Sum Test in R

 P Ehlers <[hidden email]> writes: > > so a good guess at its definition is that it is obtained from W or one > > of the others by subtracting the mean and dividing with the SD. > > > > With the SD adjusted for ties, of course. (See, e.g., Conover's book.) ...which is actually the exact SD, conditional on the set of tied ranks, not just a correction term. See my discussion with Torsten a month or so ago. --    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K  (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918 ~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html